The present invention relates to a scanning optical system used for an optical scanning unit such as a laser beam printer. In particular, the present invention relates to a scanning optical system whose imaging optical system includes an anamorphic lens that is decentered from a reference ray that reaches the center of a scanning range on an object surface to be scanned.
Such a scanning optical system is disclosed in U.S. Patent No.5,748,354. In the disclosed scanning optical system, a laser beam emitted from a laser source is deflected by a polygon mirror and forms a beam spot on an object surface such as a photoconductive drum through an imaging optical system that consists of a curved surface mirror and an anamorphic lens. The beam spot formed on the object surface moves (i.e., scans) on the object surface in a predetermined scanning direction as the polygonal mirror rotates.
In this specification, a scanning direction of the beam spot on the object surface is referred to as a xe2x80x9cmain scanning directionxe2x80x9d, a direction perpendicular to the main scanning direction on the object surface is referred to as an xe2x80x9cauxiliary scanning directionxe2x80x9d. Shapes and orientations of powers of respective optical elements will be defined on the basis of these scanning directions. Further, a ray that reaches the center of a scanning range on the object surface is defined as a reference ray.
In the scanning optical system disclosed, since a light beam incident on the polygon mirror and a light beam reflected thereby are separated in the auxiliary scanning direction and the optical path is folded by the curved surface mirror, the size of the optical system is reduced. Further, the optical axis of the anamorphic surface of the anamorphic lens is decentered from the reference ray in the auxiliary scanning direction to compensate skew distortion of the wave-front aberration that is generated since the laser beam is incident on the reflection surfaces of the polygonal mirror at an angle in the auxiliary scanning direction. The sectional shape of the anamorphic surface in the auxiliary scanning direction is an arc, and the power in the auxiliary scanning direction thereof decreases as the distance from the center increases in the main scanning direction. That is, the radius of curvature of the anamorphic surface in the auxiliary scanning direction increases as the distance from the center increases in the main scanning direction.
In the scanning optical system disclosed in the U.S. Pat. No. 5,748,354, however, since the sectional shape of the anamorphic surface in the auxiliary scanning direction is an arc, the optical system is not corrected in coma. As a result, when the laser beam on the anamorphic surface is deviated from a design area in the auxiliary scanning direction due to facet error of the polygon mirror, misalignments of the elements or the like, the focusing point of the laser beam varies in the optical axis direction, which changes the position of the beam spot and the spot size, decreasing printing performance.
FIG. 5 shows focusing points of laser beams incident on the anamorphic surface of the conventional scanning optical system at different heights in the auxiliary scanning direction. A laser beam L0 incident at the design height is focused onto the object surface. On the other hand, laser beams L1 and L2 incident at the different heights from the design height are not focused onto the object surface due to coma. The laser beam L1 is focused behind the object surface and L2 is focused in front of the object surface. As a result, the positions of the beam spots of the laser beams L1 and L2 are deviated from the position of the beam spot of the laser beam L0, and the spot sizes of the laser beams L1 and L2 become larger than that of L0. Such a defect is caused even when an effect of the facet error is compensated by employing a combination of a cylindrical lens and an anamorphic imaging optical system. In the combination, the cylindrical lens is arranged between the laser source and the polygon mirror such that the focal point thereof is located near the reflecting surface of the polygon mirror. The focal point is conjugate with the object surface.
It is therefore an object of the invention to provide an improved scanning optical system that is capable of keeping the focusing point at the same position on the object surface even if the incident point of a laser beam onto an anamorphic surface varies in the auxiliary scanning direction.
For the above object, according to the present invention, there is provided a scanning optical system, including a light source; a deflector that deflects and scans a light beam emitted from the light source; and an imaging optical system that forms a beam spot on an object surface to be scanned, the imaging optical system comprising an anamorphic lens having an anamorphic surface whose optical axis is decentered from a reference ray that reaches the center of the scanning range on the object surface, and the sectional shape of the anamorphic surface in an auxiliary scanning direction being a non-circular curved line to correct coma in the auxiliary scanning direction.
With this construction, since the coma of the anamorphic lens in the auxiliary scanning direction is corrected, the laser beam is focused at the same point on the object surface even when the incident height of the laser beam onto the anamorphic lens varies, which keeps printing performance.
The deviation of the non-circular curved line from an arc is preferably asymmetrical with respect to the reference ray in the auxiliary scanning direction. Further, a light beam incident on the deflector and a light beam deflected by the deflector may be separated in a predetermined angle in the auxiliary scanning direction. The imaging optical system may include a curved surface mirror having a predetermined power.
Still further, it is preferable that the anamorphic surface is a rotationally asymmetrical surface that is defined by a two dimensional polynomial expression as follows:       X    ⁢          (              Y        ,        Z            )        =                              Y          2                +                  Z          2                            r        ⁢                  (                      1            +                                          1                -                                                                            (                                              κ                        +                        1                                            )                                        ⁢                                          xe2x80x83                                        ⁢                                          (                                                                        Y                          2                                                +                                                  Z                          2                                                                    )                                                                            r                    2                                                                                )                      +                  ∑                  m          =          0                    ⁢                        ∑                      n            =            0                          ⁢                              B            mn                    ⁢                      Y            m                    ⁢                      Z            n                              
where X(Y, Z) is a sag, that is, a distance between a point (O, Y, Z) on a tangent plane to the anamorphic surface at the intersection point with the optical axis and a point (X, Y, Z) on the anamorphic surface in the optical axis direction, Y is a height from the optical axis in the main scanning direction, Z is a height from the optical axis in the auxiliary scanning direction, r is a radius of curvature on the optical axis, xcexais a conic constant, Bmn are coefficients.